Question

The dimension of coefficient of thermal conductivity is:
\[\begin{align}
  & A.M{{L}^{2}}{{T}^{2}}{{K}^{1}} \\
 & B.ML{{T}^{-3}}{{K}^{-1}} \\
 & C.ML{{T}^{2}}{{K}^{1}} \\
 & D.ML{{T}^{3}}{{K}^{1}} \\
\end{align}\]

Answer 1

Hint: Heat transfer coefficient is proportionality constant between the heat flux and the direction of change in heat. We know from dimensional analysis, that all the quantities can be represented in terms of their dimension.

Formula used:
$h=\dfrac{q}{\Delta T}$

Complete answer:
Coefficient of thermal conductivity is the rate of flow of heat through a solid per unit area to produce a unit temperature gradient across the solid. It is also the reciprocal of the thermal insulation.
We know that the total transfer of heat $Q$ is given as $Q=hA\Delta T$ where, $A$ is the surface area through which the heat transfers to obtain a $\Delta T$ change in temperature. And $h$ is the coefficient of thermal conductivity it is given as $h=\dfrac{q}{\Delta T}$ where $q$ is the heat flux to produce a $\Delta T$ change in temperature per meter length of the substance. Its SI unit is given as watt per meter kelvin.
The heat flux is the rate of flow of heat per unit area. While the temperature gradient is the transfer of heat i.e. the change in temperature in unit length of the given substance.
We know that the dimensions of the heat flux is given as $MT^{-3}$ and the dimension of temperature gradient is given as $KL^{-1}$
Then combining the two we get the dimension of coefficient of thermal conductivity as: $\dfrac{MT^{-3 }}{KL^{-1}}=MLT^{-3}K^{-1}$

So, the correct answer is “Option B”.

Note:
Thermal conductivity is the transfer of heat energy due to random motion of the molecules in given material. And it is the inverse of thermal resistivity. While heat transfer coefficient gives the relationship between the heat transferred across the boundary of a given body.